Big Idea

Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that âincrease by 5%â is the same as âmultiply by 1.05.â

Do Now

10 minutes

Students enter silently according to the Daily Entrance Routine. Today’s warm up assignment focuses on re-writing algebraic expressions using the distributive property, and multiplication of rational numbers. This assignment provides a great first picture of the students’ prior knowledge helpful to the aim. Students have 5 minutes to enter their multiple choice answers into Senteo clickers, providing instant data I use throughout the lesson. While students are working, I am walking around to determine if I need to show them how to multiply rational numbers (fractions and decimals). Each of the following videos shows skills I have to review with up to 50% of each of my classes this year.

First I begin by reviewing multiplying with decimals to simplify the initial expression:

To review simplifying answer choice C, I look for answers from two different students:

Then, I may show them how to multiply with fractions, given time left in this section:

To assess their understanding after I reviewed the skill and given them time to rethink and revise questions, 1 or 3, I use the Senteo clickers again to track progress toward student mastery of these skills.

All warm up assignments are clipped into students’ binders. “Task 1” worksheets are distributed. They are given 5 minutes to cut out the tickets they need to complete the scavenger hunt and to ask their neighbors or me questions about the directions. It is very important that students understand the directions, this must be made clear.

Before the lesson:

1. Tape the “FREE HINTS” all around the room, symbol side up. These locations will need to be changed in the worksheet according to your room placement).

2. Cut out groups of 5 tickets from the document include to give to students

3. Have class set of scissors ready

At the beginning of this section:

1. Distribute tasks, tickets, scissors to students

2. Set a timer for 5 minutes

Day 60 - Resource - tickets - 2013 - 11.18.docx

Day 60 - Hints for Manipulating Literal Equations - 2013 - 11.18.docx

Scavenger Hunt

20 minutes

Students may sit in groups of no larger than 4. Though allowed, they must raise their hand to ask for permission to move to another group. The aim of the scavenger hunt is to collectively earn more tickets than me by the end of class to receive a free homework pass for everyone. Each incorrect answer will cost each student a ticket that will get discarded. The only tickets that count toward my total will be those I collect from students during the scavenger hunt. I set a 20 minute timer and sit by the front of the room in a chair with a bucket to collect student tickets. The following is a list of possible hints or helpful information I provide and the cost:

I do not charge any tickets for helping students understand the directions. This means I offer no help in terms of giving answers or first steps. I offer definitions (for example, "distribution is the multiplication of an outside factor into each term in a quantity").

I charge one ticket to tell students if there are any mistakes on their solutions for each question, but i do not tell them exactly what or where the mistake is. Again, this is a good opportunity to use vocabulary (for example, "you did not combine like terms correctly")

I charge two tickets if they want me to walk them through half of the solution to a problem

Students who continually struggle with algebraic concepts may need hints in the form of guided examples on a white board. I keep one at the front along with markers and erasers. I always begin with the questions: Did you read the free hint? what did it say? what does that mean? have you done that? do you know how to distribute?

The following videos show the guided work I would show for each of the first 3 problems if academically lower students needed extra help beyond the hints offered above. Between each pause, assume that I am encouraging students to arrive at the correct answer on their own by letting them know when they are correct or incorrect, and offering guidance with nothing other than the reminder of the procedures and the use of vocabulary. For example, rather than saying "no, 3x minus x is not 4x, it is 2x" I would say, "you did not combine the variable terms correctly. The x's. What is 3x minus x?" Today's lesson calls on lots of MP4 as students twist their minds around some quantities entirely made up of variables!

video 1: help with distribution

video 2: help with clearing a denominator

video 3: help with equations containing only variables

Day 60 - Task - Manipulating Literal Equations - 2013 - 11.18.docx

Closing

10 minutes

Walk around the room checking work and answers for each problem, collecting tickets whenever the answer is incorrect. Then have students count the total number of tickets and pool them at a table in the middle of the room. If students collectively earn more tickets than me, they earn a homework pass. Remind students about the unit test in two days.

If students do not earn the HW Pass collectively as a class, they receive a HW sheet with 5 literal equations to solve. If all work is shown and all answers are correct on THIS assignment, they will individually receive a HW Pass.